Chapter 12.6

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Chapter 12.6. Surface Area and Volume of Spheres. Concept. Surface Area of a Sphere. Example 1. Find the surface area of the sphere. Round to the nearest tenth. S = 4  r 2 Surface area of a sphere = 4 (4.5) 2 Replace r with 4.5. ≈ 254.5 Simplify. Answer: 254.5 in 2.

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### Chapter 12.6

Surface Area and Volume of Spheres

Surface Area of a Sphere

Example 1

Find the surface area of the sphere. Round to the nearest tenth.

S = 4r2 Surface area of a sphere

= 4(4.5)2 Replace r with 4.5.

≈ 254.5 Simplify.

Example 1

Find the surface area of the sphere. Round to the nearest tenth.

A. 462.7 in2

B. 473.1 in2

C. 482.6 in2

D. 490.9 in2

Use Great Circles to Find Surface Area

Example 2A

A. Find the surface area of the hemisphere.

Find half the area of a sphere with the radius of 3.7 millimeters. Then add the area of the great circle.

Use Great Circles to Find Surface Area

Example 2B

B. Find the surface area of a sphere if the circumference of the great circle is 10 feet.

First, find the radius. The circumference of a great circle is 2r. So, 2r = 10 or r = 5.

Use Great Circles to Find Surface Area

Example 2C

C. Find the surface area of a sphere if the area of the great circle is approximately 220 square meters.

First, find the radius. The area of a great circle is r2. So, r2 = 220 or r≈ 8.4.

Example 2A

A. Find the surface area of the hemisphere.

A. 110.8 m2

B. 166.3 m2

C. 169.5 m2

D. 172.8 m2

Example 2B

B. Find the surface area of a sphere if the circumference of the great circle is 8 feet.

A. 100.5 ft2

B. 201.1 ft2

C. 402.2 ft2

D. 804.3 ft2

Example 2C

C. Find the surface area of the sphere if the area of the great circle is approximately 160 square meters.

A. 320 ft2

B. 440 ft2

C. 640 ft2

D. 720 ft2

(15)3r = 15

Volumes of Spheres and Hemispheres

Example 3A

A. Find the volume a sphere with a great circle circumference of 30 centimeters. Round to the nearest tenth.

Find the radius of the sphere. The circumference of a great circle is 2r. So, 2r = 30 or r = 15.

≈ 14,137.2 cm3

r 3

Use a calculator.

Volumes of Spheres and Hemispheres

Example 3B

B. Find the volume of the hemisphere with a diameter of 6 feet. Round to the nearest tenth.

The volume of a hemisphere is one-half the volume of the sphere.

Volume of a hemisphere

Answer: The volume of the hemisphere is approximately 56.5 cubic feet.

Example 3A

A. Find the volume of the sphere to the nearest tenth.

A. 268.1 cm3

B. 1608.5 cm3

C. 2144.7 cm3

D. 6434 cm3

Example 3B

B. Find the volume of the hemisphere to the nearest tenth.

A. 3351.0 m3

B. 6702.1 m3

C. 268,082.6 m3

D. 134,041.3 m3

Solve Problems Involving Solids

Example 4

ARCHEOLOGYThe stone spheres of Costa Rica were made by forming granodiorite boulders into spheres. One of the stone spheres has a volume of about 36,000 cubic inches. What is the diameter of the stone sphere?

Understand You know that the volume of the stone is 36,000 cubic inches.

Plan First use the volume formula to find the radius. Then find the diameter.

Example 4

RECESS The jungle gym outside of Jada’s school is a perfect hemisphere. It has a volume of 4,000 cubic feet. What is the diameter of the jungle gym?

A. 10.7 feet

B. 12.6 feet

C. 14.4 feet

D. 36.3 feet